Optimal control of multisurface molecular systems

We report a theoretical framework for the study of the optimal control of multisurface molecular systems via a set of nondegenerate excitation fields. The resulting control equations in the strong response regime are presented in terms of both the Liouville-space density matrix dynamics and the Hilbert-space wave function evolution. We further derive a pair of eigenequations for the optimal pump-pump fields in the pure-state control of three-surface molecular systems in the weak response regime. The globally optimal pair of pump-pump fields in this case are identified. Application to the control of a rovibronic level on the final excited surface reveals a symmetry relation within the optimal pair of pump-pump fields in the weak response regime. For numerical demonstrations, we consider the control of the I-2 molecular system involving the initial ground X, the intermediate B, and the final E surface. The target is chosen as an outgoing vibrational wave packet in the hound region of the final E electronic state. The optimal control fields in both the strong and weak response regimes are calculated and further parameterized to fit simple experimentally realizable laser pulses. (C) 1998 American Institute of Physics.